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We constantly solve problems. In many cases, there
is a prescribed way of doing something and we fit our view of the situation
and our reactions into that way of thinking and action. At other times, we may feel that
the 'rules' do not apply, or that we are facing a new problem and we must then develop our
own solution. Or the rules apply but the loss will be too great or the gain too unfair.
It is then that we search for an alternative way of dealing with a problem and come up with
a previously unused or a novel solution. In so doing, we learn and expand our parameters.

Teaching through problem solving is not always easy since many of us were taught
by remembering facts whether or not they were related to each other, whether or not we were
interested in the subject, and in some instances we were taught by rote. In fact, many
teachers may say that problem solving in their particular
subject area is not possible, not helpful, or only possible in limited parts of
the subject matter.

However, everything that can be taught may be taught from a problem solving
point of reference. The rest of this article is dedicated to this idea.

It is sometimes helpful to look at the ways in which we learn more rapidly and fully.

We learn best by solving problems or have a personal stake in the outcome. It is then
that we become interested in knowing the parameters, the details, the basis (assumptions)
on which the problem is built, and the end results.
We learn best when we have discovered the answer for ourselves.
We learn best when we have contributed the answer or have a stake in its presentation.
We learn best when we have thought out the process by which the answer is achieved.
We learn best when we have opened ourselves to different possibilities - one of which is a possible answer.
We learn best when we have come up with a possible answer whether it is correct or not. If our answer is wrong, the 'wrong' answer will cause us to retrace and find out where we went wrong in our thinking and will reinforce the answer.
We learn best when we have examined our assumptions as to what will support the answer.
Assumptions are very often the barrier to our learning and prevents us from achieving.
We learn best when we have to defend our answer against other potential answers.
We learn best when we have had to learn the supportive concepts and data which will
provide us with the correct answer.
We learn best when we have a total environmental view of the data we are learning,
its supports, its unknowns, or the controversies surrounding it.
We learn best when we have learned the different ways in which the data and the
process of deriving it are used.
We learn best when we find different ways of arriving at the same answer.

1. Provide the basis for the solving of the problem The student is often stymied by the lack of a basis from which to even begin the
problem solving process.
List the possible presumptions to be overcome in solving the problem.
Identify tools & references needed to help in arriving at a solution.
Give basic knowledge needed to begin searching for solutions.
Support off-the-wall suggestions which may have some validity or
may lead to other possibilities which are valid.
Breakdown the problem into manageable component parts.

2. Discover the interest of the students. Many students are not interested in a particular subject. It is
the teacher's challenge to illuminate the connection between the topic to be taught and the students interests.

3. Enter the world of the student. See the material to be learned from the student's viewpoint of what the student wants to do, know, experience.

4. Allow the student to create a project of personal interest which uses the material to be learned.

5. Multi-explanations or solutions.
There is always more than one explanation for a phenomenon (some have been proven
false long ago but were held to be true by the best minds of each preceding age).
Alternatively, there is more than one way to interpret what we know, or more than
one way to derive a solution. The differences should be brought up and discussed and
the students given the task of defending different positions or of deriving the
solution from different angles. Today there are many controversies still raging about
certain phenomenon. What are they in your particular field?

6. Learning can be fun. This is a caveat of learning in childhood. Remember some of
the ways in which children are taught from a unique and innovative perspective
so that learning is actually enjoyable to the child. Translate these to the subject at hand. It is never too late to enjoy the experience of learning no
matter how complicated the subject to be taught. We can learn from the simple
methods used in the earlier years of childhood. Take a list of teaching techniques from the early years. Look at them from the
perspective of the current topic. Which one fits or with a bit of imagination and innovation
can be translated or upgraded to fit the current circumstances? It is often surprising the degree to which that which
helped us learn the simpler lessons in life are still effective in later years.

7. We know that many subjects can be learned by rote. The only problem with this method
is the incredible boredom of the task and the fact that once learned we have trouble
expanding the knowledge to fit new situations. We know the material without knowing
the reason for its existence or truthfulness. We do not know the supportive knowledge
which helped our predecessors find the solution. There is no fun in learning by rote except
the high percentage on our exam grades, or in the presentation before others. But
there is little or no expansion of true knowledge.

I learned by rote parts of the Prologue to Chaucer's Canterbury Tales but to this day
have no appreciation of Middle English or how it was transformed into modern day
English, or how it limited the world view of those who spoke it, or the ability to
rhyme with it, or what other works we still have today which were written in the same
format, or how it related to the rest of the work, or to the perspective of the culture
which produced it. In fact I did not even know the meaning of the words or the phrases
until one day many years later I sat down and repeating it in my head, and attempted to
assess its meaning and its true literary value.

8. Interrelationships - It is important that the student, whatever the project is that
has been chosen, make an effort to interrelate the subject of the project with the
other topics of the subject matter. This should be more than a simple descriptive
relationship and should include ways of integrating the selected topic with the
other knowledge learned in the class. Having an individual represent a historical
figure in a debate on some topic may help learn everything about one person but
all others presented in the class may be a blank for the student at the end of the
semester.

9. Work towards the strengths of each student. It is important that each student realizes and
understands the different capabilities brought by different students to a project. No
capability or interest should be devalued. In a certain situation, each capability will
help solve a specific problem. Collective problem solving should be emphasized over
individual problem solving capabilities. Some students cannot see alternative solutions,
or any solution at all. When confronted with a potential solution, the student may be
able to contribute knowledge from other areas thus increasing interest and adding to the solution of the problem.

10. Support the discovery of what does not work. This discovery is often as important as the discover of what does work. The student can then be led to appreciate the lessons learned in the process.

We all believe in a specific order of things.
We build our perceptual concepts (assumptions) on the basis of this belief.
It is extremely difficult to change our perception because we fit our observations into the framework
of this world view. And when a particular fact does not fit, we just say that there is
not yet enough data to explain it or to account for its presence.
Some of the assumptions which we use about the forces operating in a certain
circumstance, the nature of the situation, any moral restrictions, and the probability of a certain outcome are all operating at each juncture in our
decision or non decision processes.

In the development of a problem solving method for teaching any subject, some of the
assumptions so often used in developing problem solving techniques are:
The problem must relate directly to the subject being learned
The solution must be logically derived from the problem
The problem must be a real life problem using real information as its base.

All of these are not necessarily correct. A problem with none of these assumptions
can be just as effective. The important point here is the use of or the finding
of the answers or data which is to be learned. But even this is not necessary
if the problem merely opens up the field, or expands perspective, or
creates a more conducive or neutral environment within which thinking and
exploring can take place.

The important point is that our assumptions must be checked and in certain cases
overturned in order to produce fruitful predictions and results.

In the past, many more problems were created by commonly held the assumptions behind real world events.

The assumption that the storm pattern of El Nino and La Nina are localized phenomenon
and not a worldwide phenomenon precluded any ability to forecast its occurrence.

The assumption during the baby boom that the population would continue to grow past the limits of the
world to support it (population bomb) was false and precluded
the subsequent finding that there were cycles in birth rates worldwide, new
farming and marketing methods, changes in birth patterns as populations grow
or shrink, etc.

The assumption that asbestos was not harmful to the lungs, caused much suffering
which is still being paid for.

The assumption that wings must flap like the wings of birds in order to fly
held up man's age of flight for centuries.

And on a more personal as well as societal level:

The assumption that the findings we come up with are the only possible truth
leads us to stake our wealth and lives on inaccuracies which prove
costly and in many cases fatal.

The assumption that the other side is as stupid as you think they are or are not innovative often leads
to disaster (they are usually smarter than you think, and perhaps even more so than you).

The assumption that only you have honor which must be defended at any cost,
often leads to heightened conflict.

In general, inaccurate results or predictions were caused by the following limiting assumptions:

- existence of physical limits
- limited innovative capacity of man
- only one way to do something
- methods used in testing were sufficient to indicate truth
- limits to acceptability
- change as straight line process (growth or decrease) and no other form
(i.e. cyclical, periodic off and on, upper and lower limits
causing breaks and reforming)
- strict cause and effect overriding multiple causation and results
- there is only one type of logic
- all individuals react to and see the world in the same way
- form must follow nature
- thinking limited to a specific set of conditions is usually sufficient
- reliance on strict cause and effect taking into account too few variables

Or to put some of the above in a different form, we must reject or scrutinize
carefully:
Any assumption which is culture bound
Any assumption which assumes that our particular view of the world is true
Any assumption which accepts the results of testing as true
Any assumption which causes us to accept answers which will not offend
Any assumption which assumes that current trends will continue
Any assumption which assumes that forces are operating within a specific area
Any assumption which assumes that man is limited in any way
Any assumption which is based on indeterminate facts

Examples to top
This section looks at two different examples for problem solving:
Example I - The explanation of social structure Example II - The disappearance of Neanderthal Man

Introduction
One of the problems with problem solving as a teaching method is the inability to break
out of our precepts. Since each discipline is often seen as a whole unto itself, it is
sometimes difficult to see the relationships between the different disciplines. Particularly when
one field, lets say mathematics, does not appear to lend itself well to help in our
understanding of one of the 'soft' sciences such as sociology.

For instance, if we could look at a problem from an economic or a cyclical or a mathematical
or a political or geophysical standpoint, we would not only gain new depth in perception
but would also discover possible alternative explanations of the problem.

Throughout the last 200 years, sociologists have looked at sociological phenomena through
many different lenses.

Example I - The Explanation of Social Structure

Different basic ways of looking at societysociety as a random set of acts
society as a grand design set at the beginning and played out to the end of time
society as an innate set of processes or ways of responding (instincts)
society as a complex set of cyclical processes controlled by reoccurring forces
society as a recognition and attraction on a genetic level of similarity, power, success, etc.
society as a collection of single interactions
society as a process of push and shove throughout time
society as a creation of a greater power which was set in motion and left or is still operating and guiding
society as a collection of interactive force fields which cause regional nodes and act off of one another
society as a playing out of sexual forces and dominance/submissiveness
society as a set of standard life processes (eating, reproduction, etc.) and the resultant complex of interactions
society as an evolutionary process of survival of the fittest
society as a form of follow the leader with the leaders determining the shape and destiny of mankind in any given period
society as a process of economic/market forces which push and pull the system in different directions producing a complex interplay of action
society as a constant testing of the limits of nature with changes taking place once a particular movement hits a limit and retracts or falls to start again
society as a complex set of interacting individual spheres of influence in the rational fulfillment of needs
society as an interlocking set of primitive rules which are embellished and constantly change by consensus and produce the indeterminate movements of society over time
society as an experimental process controlled by beings external to the process
society as a cooperative process of give and take which moves the process along in an attempt to survive against external limits and forces which would destroy the fabric
society as describable by a set of mathematical equations which we have not yet discovered
society as a simple set of action and reaction throughout the system creating complex buildups and troughs

Ways of Working with Example Some of these may be far fetched (or not). Select one whether you believe in it or not
and defend it against the others or against the main sociological theories of society (past and present) in the following ways:

1. Indicate the assumptions about man and about social interaction on which the theory is built
2. Show data or instances which support the view you have selected
3. Show areas which can not be substantiated but might be 'proved' given certain
parameters, findings, research.
4. Show discrepancies between the other theories and inconsistencies within each
theory which would indicate logical or other problems with the theories
5. Show how your selected theory is superior to the other theories and back it up with examples and solid evidence
6. Develop at least one test which would help substantiate your theory
7. Be able to take a test on each of the past or present theories of the field
as the semester proceeds to show that you understand the major points of the
theories, the major assumptions of man and society on which the theories are
built and their strengths and weaknesses (which of course you will use to
support your own theory)
8. Develop and indicate the logical basis for your chosen theory
9. Give at least 7 rules or ways in which your chosen theory works in society to produce what we observe in the world

Example II - The Disappearance of Neanderthal Man

Reasons for the disappearance of one species of man (Neanderthal) living in the same area
at more or less the same time as another species - Cro-Magnon Man (anatomically similar to modern man or to put it another way -
a name given to modern man, to distinguish him from Neanderthal, living in Europe between 35,000-10,000 B.P.)

More aggressive vs less aggressive - the more aggressive tended to survive.

Less varied diet which when decreased led to starvation.

Less organized living - small groups which were vulnerable against the more organized society of Cro-Magnon (modern) man.

Had fir and did not use animal skins and were less able to cope with a hard cold period

There was actually never two different species of man.

Matriarchal structure could not compete with patriarchal.

Lived in caves which were increasingly taken over by modern man and did not have constructed shelter

Genetic structure different leading to different reaction to a disease which swept through Europe

Less procreation for a number of reasons - genetic, social structure prohibiting
multiple partners in a small community and restrictive sexual norms, lower fertility, social prohibition on multiple offspring.

Gradual reduction of hunting space through encroachment by modern man on territory

Teaching and Learning via the Network
Application of "Knowledge Management" Concepts to the Interdisciplinary Area of Biotechnology
"...This project will serve as a prototype for the library's role in the application of "knowledge management" concepts to a "problem-solving" instruction model in biotechnology."
Universities of Minnesota, Wisconsin-Madison, Indiana University, Iowa State, individuals and staff University of Technology, Sydney